English

A complete characterization of exponential stability for discrete dynamics

Dynamical Systems 2020-02-11 v1

Abstract

For a discrete dynamics defined by a sequence of bounded and not necessarily invertible linear operators, we give a complete characterization of exponential stability in terms of invertibility of a certain operator acting on suitable Banach sequence spaces. We connect the invertibility of this operator to the existence of a particular type of admissible exponents. For the bounded orbits, exponential stability results from a spectral property. Some adequate examples are presented to emphasize some significant qualitative differences between uniform and nonuniform behavior.

Keywords

Cite

@article{arxiv.1710.02191,
  title  = {A complete characterization of exponential stability for discrete dynamics},
  author = {Nicolae Lupa and Liviu Horia Popescu},
  journal= {arXiv preprint arXiv:1710.02191},
  year   = {2020}
}

Comments

The final version will be published in Journal of Difference Equations and Applications

R2 v1 2026-06-22T22:05:08.293Z